Republican presidential candidate former Massachusetts Gov. Mitt Romney talks to reporters following a campaign stop at a We the People Presidential Forum at the VFW Post, Sunday, Dec. 11, 2011, in Hudson, N.H. (AP Photo/Jim Cole)

Republican presidential candidate former Massachusetts Gov. Mitt Romney arrives with his staff for a We the People Presidential Forum at the VFW Post, Sunday, Dec. 11, 2011 in Hudson, N.H. (AP Photo/Jim Cole)

Republican presidential candidate former Massachusetts Gov. Mitt Romney talks to reporters following a campaign stop at a We the People Presidential Forum at the VFW Post, Sunday, Dec. 11, 2011, in Hudson, N.H. (AP Photo/Jim Cole)

HUDSON, N.H. — Democrats and Republicans alike are accusing Mitt Romney of being out of touch after he said during this weekend’s debate that he would make a $10,000 bet with Rick Perry even as millions of Americans struggle to make ends meet in a troubled economy.

Romney shrugged off the comment Sunday — but says he’s been reminded he’s not a good gambler.

“After the debate was over, Ann came up and gave me a kiss,” Romney said, referring to his wife. “And she said, ‘there are a lot of things you do well. Betting isn’t one of them.’”

Romney’s bet — for a sum that represents more than two months’ salary for Americans with mid-range incomes —has ignited a discussion about whether Romney, a wealthy businessman whose worth is estimated at more than $200 million, is out of step with the challenges facing the millions of struggling or unemployed Americans who are having trouble providing for their families in an ailing economy.

“I would suggest to you that $10,000 is pocket change for Mitt,” said Perry, the Texas governor, who was campaigning in Iowa on Sunday. “Having an extra $10,000 to throw down on a bet seems very out of the ordinary.”

Democrats have seized on the remarks, eagerly pointing out just how much $10,000 can buy. Democratic National Committee Chairwoman Debbie Wasserman Schultz called the remark “the most out-of-touch moment in any debate so far — offering to bet Rick Perry $10,000 as casually as if it’s something he does all the time,” she said in a statement.

The remark is likely to become an issue in a general election campaign that President Barack Obama has begun to define as a fundamental philosophical struggle between fighting for shared sacrifice and curtailing government to let people fend for themselves.

“Their philosophy is simple: We are better off when everyone is left to fend for themselves and play by their own rules,” Obama said of the GOP at a major speech in Osawatomie, Kan., last week, invoking former President Teddy Roosevelt. “I’m here to say they are wrong.”

Romney’s campaign has spent most of the year focused on Obama instead of on his GOP rivals. And while former House Speaker Newt Gingrich has risen to the top of polls in several early states, Romney says he still believes he’ll be the Republican nominee.

“I’m going to get the nomination,” he told reporters here Sunday night.

When pressed about how he came up with the $10,000 bet figure, Romney wouldn’t say.

“That’s all I got,” he said, laughing with the audience of supporters standing behind him.

Romney tried to make the bet with the Texas governor after Perry accused Romney of making changes to parts of his book, “No Apology.”

“You’ve raised that before, Rick. And you’re simply wrong,” Romney said. Perry said it was true as Romney laughed and then said: “Rick, I’ll, I’ll tell you what. Ten thousand bucks? Ten thousand dollar bet?” He stuck his hand out to Perry, who wouldn’t take it.

Romney made his millions at Bain Capital, a venture capital firm. In 2008, he sometimes struggled to explain his wealth; he ended up spending more than $45 million of his own money on his failed campaign.

Romney has yet to make a significant contribution to his bid for the 2012 Republican presidential nomination. Instead, he’s tried to emphasize his focus on middle class families and the struggles they’re facing in the economy. He has pitched his tax plan as good for middle class Americans — rejecting a flat tax proposal that Perry supports because he says it would raise taxes on the middle class.

But he’s made other slip-ups on the campaign trail that have occasionally cast him as out-of touch.

In June, Romney sat and listened as, one by one, a group of unemployed Floridians told him about struggling to find work. “I should tell my story,” Mr. Romney said. “I’m also unemployed.”

Aides said he was joking. Romney hasn’t held a job in recent years — instead, he’s campaigned for other Republicans and built his own presidential campaign.

And at the Iowa State Fair in August, Romney stood on bales of hay and shouted down a questioner who accused him of favoring corporations over average Americans who rely on programs like Social Security.

“Corporations are people, my friend!” Romney shouted back.

But Romney has also made stories about his father’s Spartan upbringing a central part of his usual campaign speech as he has worked to connect with voters struggling in a bad economy. George Romney grew up poor and went on to become governor of Michigan. On the campaign trail, Romney likes to tell stories about how his father paid for his honeymoon as he went along, selling aluminum paint out of his car as the newlyweds drove.

In recent days, Romney has also started to point to his time working as a Mormon missionary in France to make the point that he can relate with those who have less. He mentioned it in Saturday’s debate and talked at length about it here Sunday.

Romney said he lived on between $500 and $600 per month.

“I lived with people in France who lived very modestly,” he said, answering a question from an audience member who wanted Romney to talk about an experience that helped shape his life.

Some of the luxuries Romney was accustomed to at home were missing. “A number of the apartments I lived in when I was there didn’t have toilets, we had instead, the little pads on the ground,” he said, to laughter. “There was a chain behind you with kind of a bucket, a bucket affair — I had not experienced one of those in the United States.”

The experience, he said, made him appreciate the U.S.

“I lived in a way that people of lower middle income in France lived,” Romney said, “and I said to myself: ‘Wow, I sure am lucky to be born in the United States of America.’”